If you're indeed talking about paper cartridges they are loaded same as copper and the later and current brass cartridges. On a Sharps open the breech, slide the cartridge into the chamber, raise the breech block which in turn slices off the back of the paper cartridge exposing the powder to the flash from the cap when the hammer is dropped. Musket caps are used.
It is wise to tip the rifle to one side or the other to dump the tail of the cartridge and the few grains of powder off the top of the breech block before capping and firing. The paper cartridge Sharps was considered an improvement over muzleloaders, and regarding rate of fire they were, but the breech seal still wasn't perfect.
Paper patch bullets are another matter. Musketmans two photos show the differences wonderfully.
Vic